Conditional entropy H(X|Y) is bounded by 0≤H(X|Y) ≤ H(X) because learning the value of Y provides information that can only reduce or leave unchanged the average uncertainty about X; it cannot increase it on average.
Conditions: X and Y are discrete random variables.
Conditional entropy H(X|Y) is bounded by 0≤H(X|Y) ≤ H(X) because learning the value of Y provides information that can only reduce or leave unchanged the average uncertainty about X; it cannot increase it on average.
Conditions: X and Y are discrete random variables.
Conditional entropy H(X|Y) measures the average remaining uncertainty or surprise about a random variable X after another random variable Y has been observed. It is defined as the expected value of the conditional self-information h(x|y) over the joint distribution of X and Y.
Conditions: X and Y are discrete random variables.; The sum is taken over the joint alphabet Ax×Ay.
Conditional entropy H(X|Y) measures the average remaining uncertainty or surprise about a random variable X after another random variable Y has been observed. It is defined as the expected value of the conditional self-information h(x|y) over the joint distribution of X and Y.
Conditions: X and Y are discrete random variables.; The sum is taken over the joint alphabet Ax×Ay.
Conditional entropy H(X|Y) equals unconditional entropy H(X) if and only if the random variables X and Y are statistically independent. In this case, knowing Y provides no information about X, so the uncertainty remains unchanged.
Conditions: X and Y are discrete random variables.
Conditional entropy H(X|Y) equals unconditional entropy H(X) if and only if the random variables X and Y are statistically independent. In this case, knowing Y provides no information about X, so the uncertainty remains unchanged.
Conditions: X and Y are discrete random variables.
The lecturer models English text as a Markov chain where the probability of the next character X depends on the previous character Y. By conditioning on context, such as knowing the previous letter is Q, the uncertainty about the next letter (often U) is greatly reduced, demonstrating how conditional entropy H(X|Y) lowers average code length.
Conditions: The source is English text.; The previous character is treated as conditioning information for the next character.
The lecturer models English text as a Markov chain where the probability of the next character X depends on the previous character Y. By conditioning on context, such as knowing the previous letter is Q, the uncertainty about the next letter (often U) is greatly reduced, demonstrating how conditional entropy H(X|Y) lowers average code length.
Conditions: The source is English text.; The previous character is treated as conditioning information for the next character.